• Search Research Projects
  • Search Researchers
  • How to Use
  1. Back to previous page

The study of arithmetic and analytic property of automorphic forms and zeta function associated with them and numerical analysis

Research Project

Project/Area Number 09640018
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Algebra
Research InstitutionIwate University (1998)
The University of Electro-Communications (1997)

Principal Investigator

KOJIMA Hisashi  Iwate University, Derartment Faculty of Education, Professor, 教育学部, 教授 (90146118)

Co-Investigator(Kenkyū-buntansha) KOMIYAMA Haruo  Iwate University, Faculty of Education, lecture, 教育学部, 講師 (90042762)
NUMATA Minoru  Iwate University, Faculty of Education, professor, 教育学部, 教授 (50028255)
MIYAI Akio  Iwate University, Faculty of Education, assistant, 教育学部, 助手 (70003960)
TAYOSHI Takao  University of electro-communications, Faculty of electro-commnucation, propessor, 電気通信学部, 教授 (60017382)
OSHIKIRI Genichi  Iwate University, Faculty of Education, professor, 教育学部, 教授 (70133931)
中嶋 文雄  岩手大学, 教育学部, 教授 (20004484)
吉岡 正典  電気通信大学, 電気通信学部, 助手 (90272749)
中村 健一  電気通信大学, 電気通信学部, 助手 (40293120)
小藤 俊幸  電気通信大学, 電気通信学部, 助教授 (30234793)
伊東 裕也  電気通信大学, 電気通信学部, 助教授 (30211056)
Project Period (FY) 1997 – 1998
Project Status Completed (Fiscal Year 1998)
Budget Amount *help
¥2,900,000 (Direct Cost: ¥2,900,000)
Fiscal Year 1998: ¥1,300,000 (Direct Cost: ¥1,300,000)
Fiscal Year 1997: ¥1,600,000 (Direct Cost: ¥1,600,000)
Keywordsmodular forms of half integral weight / modular forms / zeta functions / critical values of zeta functions / Fourier coefficients of modular forms / Riemannian fo / compact leaf / モジュラー形式 / 半整数の重さのモジュラー形式 / 保型形式
Research Abstract

(1) Under assumptions of the multiplicity one theorem of Hecke operators, H.Kojima deduced an explicit relation between the square of Fourier coefficients a(4n) at a. fundamental discriminant 4n of modular forms f(x)=SIGMAepsilon(-1)^kn=0,1(4), n>0 a(n)e[nzl belonging to the Kohnen's space of half integral weight (2k+1)/ and of arbitrary odd level N with primitive character x and the critical value of the zeta function of the modular form F which is the image of f under the Shimura correspondence PSI.Our methods of the proof are the same as those of Shimura. We treated the excluding case in the Shimura's paper concerning Fourier coefficients of Hilbert modular forms of half integral weight and our results gave a generalization and development of Shimura' results. Moreover, using this method, we derived an analogous results in the case of Maass wave forms of half integral weight belonging to Kohnen's spaces.
(2) Oshikiri proves that if the codimension of a bundle-like foliation F of a Riemannian manifold (M, g) with positive sectional curvature is even, then F hasa compact leaf, and that if the codimension of F is odd, then F has a leaf whose closure is a codimension (q- 1) closed submanifold of M.
(3) As ingredients for the order problem of the Riemann zeta-function, Miyai investigated alternative explicit formulas for various arithmetic exponential sums relating to the problem. On constructing the cosinus form for the Atkinson phase function f(T, n), he gave an explicit formula for |zeta(1/+iT)|^2.
(4) Tayoshi considered the equation of the vibration of a elastic string in 3-dimensional space. Supposing Hooke's law and certain Lagrangian density, on the basis of analytic mechanics, he derived a system of nonlinear partial differential equations, which, in our expectation, describes the vibration of the string. Moreover, he obtained some stationary solutions.

Report

(3 results)
  • 1998 Annual Research Report   Final Research Report Summary
  • 1997 Annual Research Report
  • Research Products

    (24 results)

All Other

All Publications (24 results)

  • [Publications] H.Kojima: "The formula for the dimension of the spaced of vector valued holomorphic automorphic forms on the unitary group SV(l,p)" Kyushu J. of Math.51. 57-76 (1997)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] H.Kojima: "Fourier coefficients of modular forms of half integral weight, periods of modular forms and the special values of zeta function" Hiroshima Math J.27. 361-371 (1997)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] H.Kojima: "On explicit construction of Hillert-Siegel modular forms of degree two" Acta Arith.LXXX1. 265-274 (1997)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] H.Kojima: "Remark on Fourier coefficients of modular forms of half integral weight belonging to Kohneu's spaced" to appear in J.Math.Soc.Japan. (1999)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] H.Kojima: "Remark on Fourier coefficients of modular forms of half integral weight belonging to Kohneu's spaces II" to appear in Kodai Math.J.22. 99-115 (1999)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] G.Oshikiri: "Codimension-one foliation and oriented graphs" to appear in Tohoku Math.J.(1999)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] H.Kojima: "The formula for the dimension of the spaces of vector valued holomorphic automorphic forms on the unitary group su(1, p)" Kyushu J.of Math. 51. 57-76 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] H.Kojima: "Fourier coefficients of modular forms of half integral weight, periods of modular forms and the special values of zeta functions" Hiroshima Math.J.27. 361-371 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] H.Kojima: "On explicit construction of Hilbert-Siegel modular forms of degree two" Acta Arith.LXXXI.3. 265-274 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] H.Kojima: "Remark on Fourier coefficients of modular forms of half integral weight belonging to Kohnen's spaces" J.Math.Soc.Japan. (to appear).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] H.Kojima: "Remark on Fourier coefficients of modular forms of half integral weight belonging to Kohnen's spaces II" Kodai Math.J.(to appear).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] H.Kojima: "On Fourier coefficients of Maass wave forms of half integral weight belonging to Kohnen's spaces" Tsukuba J.Math.(to appear).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] G.Oshikiri: "Codimension-one foliations and oriented graphs" Tohoku Math.J.(to appear).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] K.-I.Nakamura, H.Matano, D.Hilhorst and R.Schatzle: "Singular limit of a reaction-diffusion equation with a spatially inhomogeneous reaction term" Journal of Statistical Physics.(to appear).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] H.Kojima: "Remark on Fourier coefficieuts of modular forms of half integral weight belonging to Kohnen's spaces" J.Math.Soc.Japan. (発表予定). (1999)

    • Related Report
      1998 Annual Research Report
  • [Publications] H.Kojima: "Remark on Fourier coefficieuts of modular forms of half integral weight belonging to Kohnen's spaces II" Kodai Math,J. 22(発表予定). 99-115 (1999)

    • Related Report
      1998 Annual Research Report
  • [Publications] H.Kojima: "On Fourier coefficients of Maass wave forms of halt integral weight belonging to Kohnen's spaces" Tsukuba J,Math.(発表予定).

    • Related Report
      1998 Annual Research Report
  • [Publications] G.Oshikiri: "Co dimension-one-foliations and oriented graphs" Tohoku Math,J.(発表予定). (1999)

    • Related Report
      1998 Annual Research Report
  • [Publications] Hisashi Kojima: "The formura for the dimension of the spaces of vector-valued holomorphic automorphic forms on the unitary group SU(1,p)" Kyushu J.of Math.Vol.51. 57-76 (1997)

    • Related Report
      1997 Annual Research Report
  • [Publications] Hisashi Kojima: "On explicit construction of Hilbert-Siegel modular forms of degree two" Acta Arithmetica. LXXX1.3. 265-274 (1997)

    • Related Report
      1997 Annual Research Report
  • [Publications] Hisashi Kojima: "Fourier coefficients of modular forms of half integral weight,periods of modular forms and special values of ζ functions" Hiroshima Math.J.27. 361-371 (1997)

    • Related Report
      1997 Annual Research Report
  • [Publications] Hiroya Ito: "Optimal koin's inequalities for divergence-free vector fields with applicational in compressible linear elastodynamics" to appear in Japan.J.Ind.Appl.Math.

    • Related Report
      1997 Annual Research Report
  • [Publications] Yoshiyuki Koto: "The Stability of Natural Runge-Kutta Methods for Noninear Delay differential eguations" Japan.J.Ind.Appl.Math.14. 111-123 (1997)

    • Related Report
      1997 Annual Research Report
  • [Publications] Toshiyuki Koto: "NP-Stability of Runge-Kutta Methods Based on classical quadrature" BIT. 37. 870-844 (1997)

    • Related Report
      1997 Annual Research Report

URL: 

Published: 1997-04-01   Modified: 2016-04-21  

Information User Guide FAQ News Terms of Use Attribution of KAKENHI

Powered by NII kakenhi